A model-based framework, due originally to R. A. Fisher, and a design-based framework, due originally to J. Neyman, offer alternative mechanisms for inference from samples to populations. We show how these frameworks can utilize different types of samples (nonrandom or random vs. only random) and allow different kinds of inference (descriptive vs. analytic) to different kinds of populations (finite vs. infinite). We describe the extent of each framework's implementation in observational psychology research. After clarifying some important limitations of each framework, we describe how these limitations are overcome by a newer hybrid model/design-based inferential framework. This hybrid framework allows both kinds of inference to both kinds of populations, given a random sample. We illustrate implementation of the hybrid framework using the High School and Beyond data set. (Contains 2 tables, 3 figures and 15 footnotes.)